Abstract: The isomorphism identification of epicyclic gear train can eliminate the repeated structure in the process of synthesis, which is of great significance to the design and synthesis of epicyclic gear train. Aiming at the problem of isomorphism identification of epicyclic gear train, a new method to establish equivalent circuit to identify the isomorphism of epicyclic gear train is proposed. The topological structure of epicyclic gear train is described by bicolor topological graph to avoid pseudo-isomorphism. According to the similar topological constraint characteristics of the circuit network and topological graph of epicyclic gear train, the corresponding topological graph is transformed into an equivalent circuit with the same constraints, and isomorphism identification is preliminarily carried out according to the equivalent circuit elements. The homogeneous linear equations of the basic loop current of the equivalent circuit are presented by the loop current method, and the coefficient matrix retains the structural characteristics of the equivalent circuit. It is proved that the same eigenvalues of the coefficient matrix can be regarded as a necessary and sufficient condition for the isomorphism of the equivalent circuit. The simplicity and reliability of the method are verified by some examples.

Key words: epicyclic gear train, isomorphism identification, bicolor topological graph, equivalent circuit, loop current method